I'm not
currently teaching a course that uses this tutorial, but I've left it up
because a few people out there have found it useful. Please send any
criticisms or suggestions to me at danby@u.washington.edu. Best, Colin
Danby

1. Nature of the
Model

Any model makes some things
endogenous (determined within the model) and some things exogenous (determined
outside the model). Let's go back to the income expenditure model, which
you learned in intro macro. In that model Y was endogenous. G and Ip were exogenous. Solving for equilibrium Y required
finding the solution to only one equation: Y = C + Ip
+ G.

Only Y was endogenous in the
income-expenditure model. The IS-LM model makes both Y and r endogenous. The
key advantage of this is that we can have r determine Ip.
Since the level of planned investment is important in the real world and varies
a lot, it's nice to have a model in which that is not just set exogenously.

So what determines r? This model attempts to
capture Keynes' insights about the money market, which you also studied in
intro macro. We regard r as the outcome of the interaction between money demand
and money supply. This is why IS-LM is essentially two models stuck together: a
model of the goods market, and a model of the money market.

2. Equilibrium

This can be a difficult model
to learn. There is a danger that you'll concentrate so hard on the mechanics of
it that you'll lose sight of how the model relates to the real world.

Macro models do not claim that the economy is
always at equilibrium. What they do claim is that if the economy is not at
equilibrium, it will move toward equilibrium. (Near the end of this
tutorial are some animations that try to show this movement.) Thus in the
income-expenditure model, if G rises a series of
events will raise Y, until a new equilibrium is reached at which there is
enough extra savings. Review: Macro Notes
Section 1.9.

The notion of equilibrium, and how the macroeconomy is supposed to move toward it, is the key to
understanding the IS-LM model. This model is composed of a goods market and a
money market. You can think of it as embodying two ideas:

a. Depending on the interest
rate (which determines Ip), there will be an
equilibrium level of Y. If Y is below this equilibrium level, it will tend to
rise. If Y is above this equilibrium level, it will tend to fall.

b. Depending on the level of transactions
demand for money (set by Y) there will be one interest rate that equilibrates
the money market. If r is above this level, it will tend to fall. If r is below
this level, it will tend to rise.

What makes things interesting,
but also difficult, is that both r and Y can change. Below we will develop our
separate models of the goods and money markets, and then put them together. If
the terminology of goods and money markets is not familiar, review it here: Macro Notes Section 4.1.

3. Goods Market
(IS)

Take the income-expenditure
model, which you reviewed above (go back if you didn't). If Ip
rises, equilibrium Y rises, right?This
was because a higher level of demand for capital goods caused more to be made, more
workers got hired, they bought more stuff, and so
on. Add to this the idea that Ip rises when r
falls -- the cheaper it gets to borrow money, the more new capital investment
projects firms undertake.

If
r falls, Ip rises. When Ip
rises, equilibrium Y rises, as shown in the income expenditure model.

If
r rises, Ip falls and equilibrium Y falls.

The different values of r,
and the resultant equilibrium values of Y, give us a set of Y,r points that represent "goods market"
equilibrium -- a situation in which AD=AS.

Here are some graphs
that show how we get this set of points. Click the graphs to enlarge them.

This is theory you already know from intro
macro. All we've done is add a new graph with Y on the horizontal axis and r on
the vertical axis. The set of (Y,r)
combinations that represent goods market equilibrium fall along a line in our
graph.

The best way to think about that IS line is
as a border -- a boundary in (Y,r)
space between points at which AD < AS and Y will tend to fall, and the
points at which AD > AS and Y will tend to rise.

Here is another
graphical way to represent the IS curve. This picture is essentially the same
as the derivation of the IS curve that you looked at above, except that we
glued some of the graphs together at their common axes (turning some upside
down), to get a "four quadrant" derivation. The depiction of IS
itself emphasizes that the line is a frontier between the Y,r points at which Y is below equilibrium, and the (Y,r) points at which it is above its equilibrium level.

It should be apparent from the graphical
derivations that if G changes, then the (Y,r)
points that equilibrate the goods market change too. In graphical terms, a rise
in G will shift IS right, while a fall in G will shift it left.

Additionally, note that the sensitivity of Ip to r will affect the slope of IS. If planned investment
is highly sensitive to r, then a small change in r will mean a large change in
Y, and IS will be almost horizontal. If planned investment is hardly affected
at all by r, then it will take a large change in r to get much change in Y, and
IS will be almost vertical.

To recap before moving on: the above is
really just the income-expenditure model plus the idea that r affects Ip. Note that we are reasoning from r to
Y, via Ip.

4. Money Market
(LM)

This is also built out of
theory you learned in intro macro, but it's a little harder. Try to keep the
reasoning about the money market strictly separate in your mind from what you
just learned about the goods market.

The notion of equilibrium here is a situation
in which money demand equals money supply. Money demand comes from two
sources: transactions and speculative demand. Money supply we will regard as
exogenously set by the central bank, acting on the commercial banking system.

An extensive review of what money is and how
its supply is set can be found here: Macro
Notes Part 2.

You should remember that if bond prices rise,
that's the same thing as saying interest rates fall. If that's not clear,
review it here: Macro Notes Section 3.5.

If the money market is out of equilibrium,
the interest rate changes. You may remember that this happens because
individuals hold wealth in a portfolio consisting of money and bonds:

When
people finding themselves holding more money than the want, they try to
turn some of it into bonds by buying bonds, which pushes up bond prices
(which is the same thing as r falling).

When
people find themselves holding less money than they want, they they try to sell bonds to raise money, which pushes
down bond prices (which is the same as r rising).

The amount of money held by
everyone actually never changes during this story -- rather, the change in r makes them willing to hold the money they actually
hold. In the first case above, as r falls the advantage of holding wealth
as bonds falls, and people stop wanting them as much, which means they're
content to hold the money they actually hold. In the second case above,
as r rises the advantage of holding bonds rises, which means people stop
wanting to hold more money. Take some time to think about this -- the key
to the argument is this very stark, very simple money/bonds portfolio choice
faced by everyone in the economy. (This is a good time to remember the stock/flow distinction: In the
money market we are talking about stock quantities (money supply, money demand,
bonds), and our equilibrium is a stock equilibrium. In the goods market
above we are talking about flow quantities (Ip, Y, S,
G, T) and our equilibrium is a flow equilibrium.
So keep the two stories straight and strictly separate.)

Got all that? Then here's the key: the
reasoning in this model goes from Y, to transactions demand for money, to an
attempt at portfolio adjustment, to a change in the interest rate.

A
rise in output (Y) is also a rise income (remember Y means both). A
rise in income raises people's transactions demand for money. Higher
demand for money means people want to hold portfolios consisting of more
money and less bonds at any point in time. People attempt this
readjustment by selling bonds. Selling bonds lowers the bond price,
which is the same thing as raising the interest rate.

A
fall in Y lowers transactions demand for money. People try to adjust
by buying bonds with money -- changing their portfolios so they will hold
more bonds, less money. As they try to do this the bond price rises,
which is the same thing as saying r falls.

With those ideas, we
can determine the r that will equilibrate the money market for any Y. Here is a
series of graphs that derives the LM curve.

The best way to think about that LM line is
as a border -- a boundary in Y,r
space between points at which Md < Ms and r will
tend to fall, and the points at which Md > Ms and
r will tend to rise. Here is a four-quadrant derivation that emphasizes
this.

It should be apparent from the graphical
derivations that a change in the money supply will change the (Y,r) points at which the money market
is in equilibrium. In graphical terms an increase in
Ms shifts LM down, while a decrease shifts it up.

Additionally, note that the degree to which
speculative demand for money responds to changes in r will affect the slope of
the LM curve. If only a small change in r brings large changes in speculative
demand, then LM will be almost horizontal. If a very large change in r is
required to change speculative demand for money, LM will be close to vertical.

Note, before moving on, that in the money
side of this model we are reasoning from Y to r. Depending
on Y, r changes because of the effects of a given level of Y on the money
market.

5. Assembling
the Model (IS and LM)

So far, we've drawn two
different boundaries in Y,r
space:

Note again, as you look at these pictures,
that:

on
the goods market, or IS, side of the model we go from r to
Y. Pick any value of r, and draw a horizontal line across the graph
at that value of r. The line will cross the IS boundary at some
point. If the interest rate is at that level and output (Y) is to
the left of that boundary, it will tend to rise -- output and employment
will go up. If Y is to the right of that boundary, it will tend to
fall -- output and employment will go down.

on
the money market, or LM, side of the model we go from Y to
r. Pick any value of Y, and draw a vertical line up the graph at
that value of Y. The line will cross the LM boundary at some point.
If output is at that level and r is above that boundary, it will tend to
fall. If r is below that boundary, it will tend to rise.

Putting the two pictures
together gives us this geography:

Try to think of this not just
as a couple of lines crossing on a graph, but as a 2-dimensional space in which
the national economy sort of skates around, with its total output and its
interest rate changing. Once you have that idea, add the notion that the
IS and LM boundaries tell you about the forces acting on the national economy
at any particular point in this space. (For another way to visualize
this, look at this
picture at Prof. Andreas Thiemer's"IS-LM
Model: A Dynamic Approach".)

In intro macro, we noticed that the goods and
money markets interacted with each other (Review: Macro Notes Section 4.5). The IS-LM model
simply gives us a more formal way to examine these interactions.

These animations show the ways in which
fiscal and monetary policy may have effects on output and the interest rate.
They also emphasize the fact that adjustment toward a new equilibrium is not
instantaneous.

In general, in the stories we start by
assuming equilibrium in both markets -- in other words, our macroeconomy
has settled down to the one (Y,r) combination that
equilibrates both markets at once. Then we change conditions in one or
the other market. What that means is that the (Y,r) geography shifts and our old (Y,r)
point is no longer an equilibrium. So we start moving, spiralling gently counterclockwise toward the new
equilibrium point.

The stories told in the animations boil down
to this:

Fiscal Policy Stories:

1. G changes, raising or
lowering AD (throwing goods market out of equilibrium)2. As firms respond, Y changes (and a multiplier
process is set off, as AS (Y) adjusts to AD)3. BUT: as Y changes, Md(t) changes, throwing the
money market out of equilibrium.4. The change in Md(t)
changes r(Note: the degree to which speculative demand for
money changes as r changes determines how much r changes as a result of this
process.)5. the change in r
affects Ip, which affects Y through the multiplier,
modifying initial changes in Y.(Note: the sensitivity of Ip
to r determines how great this change is.)

Monetary Policy Stories:

1.
Ms changes, throwing money market out of equilibrium2. As people either buy or sell bonds to reflect
their portfolio preferences, the bond price rises or falls, with r moving the
opposite way.(Note: the degree to which speculative demand
for money changes as r changes determines how much r changes as a result of
this process.)3. BUT: as r changes, Ip
changes, throwing the goods market out of equilibrium.(Note: the sensitivity of Ip
to r determines how great this change is.)4. Working through the multiplier, the changed Ip changes Y.5. The change in Y will affect Md(t), modfiying initial effects on r.

If
you can learn these stories as sequences of events, you have a basic grasp of
the IS-LM model. Although the pictures are nice, it's more important to be able
to follow a concrete story. The geometry is just a supplement, a learning aid.
If you memorize the geometry and don't learn what it means, you're not learning
economics.

Graphically, the notes in parentheses would
affect the steepness or flatness of the IS and LM curves (noted in earlier
sections).

6. Supplemental
Notes for the Curious: History and Critiques

The origin of this model is a
paper by John Hicks
titled "Mr.
Keynes and the Classics," which appeared in the journal Econometricain
1937. It was an effort to turn some of
the insights in John
Maynard Keynes'pathbreakingGeneral
Theory of Employment, Interest, and Money(1936) into a mathematical
model. Keynes liked Hicks' article, but it’s hardly a full embodiment of
Keynes' thinking. It became popular in
textbooks.(See Kerry A Pearce. and
Kevin D. Hoover, “After the Revolution: Paul Samuelson and the Textbook
Keynesian Model” pages 183-216 in Allin
Cottrell and Michael Lawlor, eds., New Perspectives on Keynes, Duke
University Press, 1995.)

The model has some internal problems, particularly because
of the way it tries to link a flow model (the IS side, where flows adjust) and
a stock model (the LM side, where stocks adjust).These two models really live in different
kinds of time. Equilibration on the LM side is very rapid, while equilibration
on the IS side may take months. The "r" on the LM side is a
short-term rate; the key "r" for the IS side is going to be a
longer-term rate. Hicks addressed these concerns 43 years later in his 1980
article "IS-LM: Anexplanation"
(Journal of Post Keynesian Economics,
3:2, 139-54, reprinted in Hicks, ed.,Money, Interest and Wages: Collected Essays on Economic
Theory, vol. II, Oxford: Basil Blackwell, pp. 318-331).He concluded
that the problems are important enough that the model is of little use for forward-looking
policy analysis.

A more formal presentation of the model, plus
incisive discussion of subsequent debates over it, can be found
here. If you’re interested
in Keynes’ thought, one of the best introductions is Hyman Minsky’s 1975 book John Maynard Keynes
(New York: Columbia University Press),
which clarifies the differences between Keynes and the versions of his work
that you will encounter in most textbooks.Robert
Skidelsky has written an excellent three-volume
biography of Keynes; if you want something shorter try Skidelsky’s
136-page Keynes (Oxford University
Press (Past Masters), 1996).If
you’re interested in current heterodox economics, one place to start is
the Post-Autistic Economics Network.